What should I do with a watch that was gifted to me by a girl for whom I did not reciprocate the same feelings, especially since she refused to take it back, and my sister has cut ties with her? And is it permissible for me to keep it according to Islamic law?

If a woman gives you a watch as a gift, hoping you will marry her, there is no harm in benefiting from it. However, if her intention is to tempt you and draw you into a forbidden relationship, then you must return it and cut ties with her. It is not permissible to celebrate birthdays, as they are a reprehensible innovation.